# Powerpoint Problems

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```					PowerPoint Problems
Chapter 14 – Problem 4

Problem Statement

Worksheet Prob. 14-4 lists electrical resistance measure values for 50 samples of size 5 that were
taken from Babbage Chips, Inc.’s computer chip making process over a 25-hour period. The
statistical process control study is designed to answer several questions that management has,
including:

a. What descriptive statistical information, in the form of the mean and standard deviation, can
be found from the study?
b. What are the control limits of the process and how can they be used to construct the
preliminary x and R charts, using the first 30 samples?
c. Is the process under control at that point?
d. Using the remaining 20 samples, when plotted on the control chart using the control limits
calculated earlier, does the process appear to be in statistical control?
e. Why or why not?
f. What should be done if it is not under control?

Data
Complete sample data for 50 samples was provided on the student disk. Below are the
summarized sample statistics.

Summarized Data
Sample Numbers
DATA                1       2       3      4       5      6            7        8       9       10
Sample Means      9.290   9.010   9.251  8.607   8.998 10.427        8.317    8.334   9.580   9.374
Sample Ranges     3.241   4.840   2.442  2.812   3.961 3.890         2.467    1.299   1.764   1.930

11      12      13       14       15       16      17       18      19      20
Sample Means      8.624   9.269   10.057   9.498    9.984    9.068   9.482    8.698   9.240   8.849
Sample Ranges     1.825   2.193   2.573    3.280    1.298    1.548   3.433    1.382   2.179   2.340

21      22      23       24       25       26      27       28      29      30
Sample Means      9.233   8.660   8.314    9.695    8.935    9.625   9.551    9.312   9.743   8.062
Sample Ranges     2.810   2.890   2.376    2.225    2.628    1.442   3.063    3.413   3.101   1.648

31      32      33       34       35       36      37       38      39      40
Sample Means      8.345   8.087   8.865    8.258    9.435    8.530   9.165    8.183   8.592   8.986
Sample Ranges     1.548   3.063   1.925    2.890    4.025    1.429   2.380    3.245   2.223   2.868

41      42      43       44       45       46      47       48      49      50
Sample Means      9.130   9.440   8.560    9.021    9.972    8.915   8.663    9.162   8.777   9.119
Sample Ranges     1.700   2.243   1.129    0.963    1.655    3.494   3.347    2.041   0.494   3.408
Analysis
Descriptive statistics

Based on all 50 samples, descriptive statistics are shown below.

Descriptive Statistics - Problem                                                              Bin      Frequency
14-4
6.0            0
Mean                                       9.046                                              6.6            3
Standard Error                             0.070                                              7.2            9
Median                                     9.011                                              7.8           23
Mode                                       9.215                                              8.4           36
Standard                                   1.103                                              9.0           52
Deviation
Sample Variance                             1.218                                              9.6          48
Kurtosis                                   -0.323                                             10.2          44
Skewness                                    0.071                                             10.8          19
Range                                       5.716                                             11.4          12
Minimum                                     6.341                                             12.0           3
Maximum                                    12.057                                             12.6           1
Sum                                       2261.440
Count                                     250.000
Conf.                                       0.137
Level(95.0%)

Histogram

60
50
Frequency

40
30                                                                                 Frequency
20
10
0
10.2
10.8

11.4
12.0
12.6
6.0
6.6
7.2

7.8
8.4
9.0

9.6

Bin
Control Charts

a. Calculation of control limits using only the first 30 samples:

For the Center Lines, CL x : x = 9.170; CLR: R = 2.543

Control limits for the x - chart are: x ± A2 R

UCL x = x + A2 R = 9.170 + ( 0.577) 2.543 = 10.637

LCL x = x - A2 R = 9.170 - ( 0.577) 2.543 = 7.702

For the R-chart:

UCLR = D4 R = (2.114) 2.543 = 5.376

LCLR = D3 R = 0

b.      When using these control limits to monitor the last 20 samples, there is one unusual
occurrence, with several out of the last eight samples below the centerline, indicating a
probable out-of-control condition.
Prob. 14-4B X-bar Chart                  Averages
Lower control limit
Upper control limit
Center line
11
10.5
10
Averages

9.5
9
8.5
8
7.5
7
6.5
6
1       3       5       7    9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sample number

Prob. 14-4B R-Chart                  Ranges
Lower control limit
Upper control limit
Center line

6

5
Ranges

4

3

2

1

0
1     3        5       7       9       11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sample number
Conclusions

a. What descriptive statistical information, in the form of the mean and standard deviation, can
be found from the study?

          The histogram shows the “classic” bell curve shape.

b. What are the control limits of the process and how can they be used to construct the
preliminary                   x and R charts, using the first 30 samples?
   Control limits are shown above

c. Is the process under control at that point?

   Results from only the first 30 samples of 5 for Babbage show that both the x and R
charts are apparently in control. (See spreadsheet C14-4AXR.xls in the instructors’
manual for details).

d. Using the remaining 20 samples, when plotted on the control chart using the control limits
calculated earlier, does the process appear to be in statistical control?
e. Why or why not?

   When using these control limits to monitor the last 20 samples, there is one unusual
occurrence, with seven out of the last eight samples below the centerline, indicating a
probable out-of-control condition. (See spreadsheet C14-4BXR.xls in the instructors’
manual for details).

f. What should be done if it is not under control?

   Assignable causes should be sought.

Recommendations

The report to management would include the analysis presented above. It should also include the
recommendations that he/she:

   Monitor the process, after assignable causes mentioned above, are traced. If they are
obviously due to non-recurring factors, which will show that the process would have been
in control. If it is felt that control limits are still realistic, continue to monitor the process
without changing them.
   Perform a process capability study to determine if improvements should be made.

```
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